Linear independent Solutions to Differential Eq.

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$Old$ November 3rd, 2009, 07:47 AM

charikaar $charikaar is offline$

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$Default$ Linear independent Solutions to Differential Eq.

Hi,

Could you please help me with part (i) and (ii) on this sheet
http://www.maths.qmul.ac.uk/~cchu/MTH6122/lode094.pdf

If y1; : : : ; yn are solutions to (1). How do i get solutions to (2) i.e solutions as vectors.

I know if y is solution to (1) then the corresponding solution for (2) is given the vector (y,y',y'',y''',......y^n-1)^T. I know Wronskian is given by:

$Wr(y_1,...,y_n)=det\left(\begin{array}{ccc}y_1&\cdots&y_n\\y_1\prime&\cdots&y_n\prime\\\vdots&\vdots&\vdots\\y_1^{(n-1)}&\cdots&y_n^{(n-1)}\end{array}\right)$

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